CALCULUS 2 FIVES SHEET

F=Fun at home I=Incunabula V=Variety E=Endeavors S=Specimens

Monday, 5/9 - FINISH MOVIE
PRINT THE NOTES ON DIFFERENTIAL EQUATIONS AND BRING THEM
TO CLASS TOMORROW.
HOMEWORK IS NOW WORTH 800 POINTS EACH !!!!!
Tuesday, 5/10 - PRINT THE NOTES ON DIFFERENTIAL EQUATIONS AND BRING THEM
TO CLASS TODAY.
HOMEWORK IS NOW WORTH 800 POINTS EACH !!!!!
F #151 Solve the following first order linear differential equations:
1. ex + 2exy = 1 2. x + 3y = 3. x + 2y = 1 –
ANSWERS: 1. e–x + Ce–2x 2. 3. – +
I 1. The slope of the line given by the equation 6x– 2y+ 7= 0 is
(A) •(B) 3 (C) 6 (E) 7
2. If ƒ(x)= x2, then ƒ(x+ 1) = (A) x2+ 1 (B) x2+ x (C) x2+ x+ 1 •(D) x2+ 2x+ 1 (E) x3+ x2
V None
E Solving first order linear differential equations.
S Solve: x + y = ex ans: + y = , P(x) = , Q(x) = ––> = = ln x
I(x) = e= eln x = x –––>
= = =
Wednesday, 5/11
F #152 Solve the following first order linear differential equations:
1. + (tan x) y = cos2x 2. (1 + x) + y = 3. 2 = ex/2 + y 4. x y ' – y = 2x ln x
ANSWERS: 1. sin x cos x + C cos x 2. 3. x ex/2 + C ex/2 4. x(ln x)2 + Cx
I 1. If logx = 5, then (A) x= 15 • (B) x= 35 (C) x= 53 (D) x3= 5 (E) x5= 3
2. If the distance between the points (x,11) and (1,– 1) is 13, then which of the following could be a value of x ? (A) 2 (B) 4 (C) 5 • (D) 6 (E) 12
V None
E Solving first order linear differential equations.
S Lots!!
Thursday, 5/12
F #153 Solve the following first order linear differential equations:
1. e2x y ' + 2e2x y = 2x 2. x = – 2y 3. (x – 1)3 + 4(x – 1)2 y = x + 1
4. (cos x) + (sin x) y = cos x
ANSWERS: 1. x2 e–2x + Ce–2x 2. 3. 4.(cos x)(ln|sec x+tan x| +C)
I 1. If ƒ(x) = x2, then ƒ(x+ 1) = (A) x2+ 1 (B) x2+ x (C) x2+ x+ 1 • (D) x2+ 2x+ 1 (E) x3+ x2
2. The height of a right circular cylinder is four times the radius of its base, and its volume is 108. What is the height of the cylinder ? • (A) 12 (B) 6 (C) 3 (D) 12
V None
E Solving first order linear differential equations.
Friday, 5/13
F #154 Solve the following first order differential equations
(1 & 2 are homogeneous, 3 & 4 are linear) :
1. = – 2. = 3. = ex – y 4. x – 3y = x2
ANSWERS: 1. x3 + 3xy2 = eC 2. y = 3. y = ex + Ce–x 4. y = –x2 + Cx3
I 1. The solution set to the system: is
A) {0,2} B) {0,0} C) D) {8,3} •E) infinite number of solutions
2. divided by equals A) B) C) •D) E)
V None
E Solving first order homogeneous differential equations.
S
Monday, 5/16
#154.5 Worksheet #51 1-6 ALL
I
1. In the figure above, what is the value of x ? 65
2. If (x + 2)2 = 25 and x > 0, what is the value of x2 ? 9
V None
E Solving first order homogeneous and linear differential equations.
S Get ready for the test!!
Tuesday, 5/17
F#155 Solve the following first order differential equations:
1. 2 – y = ex/2 2. x dy+ y dx = sin x dx 3. = 4. dx + x cos dy = 0 5. ex + 2exy = 1 6. + (tan x) y = cos2x 7. x y ' – y = 2x ln x 8. = –
ANSWERS:
1. y = ex/2 (x + C) 2. y = 3. ln(x2 + y2) + tan–1= C 4. sin =
5. e–x + Ce–2x 6. sin x cos x + C cos x 7. x(ln x)2 + Cx 8. x3 + 3xy2 = eC
I 1. A triangle has a base of length 13 and the other two sides are equal in length. If the lengths of the sides of the triangle are integers, what is the shortest possible length of a side? 7
2. In a stack of six cards, each card is labeled with a different integer 0 through 5. If two cards are selected at random without replacement, what is the probability that their sum will be 3 ? ANSWER: 2/15 or 0.133
V None
E Solving first order homogeneous and linear differential equations.
S Get ready for the test!!
Wednesday, 5/18
F #156 Solve the following first order differential equations:
1. ex + 2exy = 1 2. + (tan x) y = cos2x 3. x y ' – y = 2x ln x 4. = –
ANSWERS: 1. e–x + Ce–2x 2. sin x cos x + C cos x 3. x(ln x)2 + Cx 4. x3 + 3xy2 = eC
I None
V None
E Solving first order homogeneous and linear differential equations.
S Notes problems for test tomorrow.
Thursday, 5/19 TEST TODAY !!!!! 3,000 points
Homework Packet is due 151-156 worth 1,400 points !!!!!
F #157 Non-seniors: start working on Vector Worksheet 1-98 all.
Vector Worksheet will be due the day of the FINAL EXAM and is worth 1,000 points
Seniors –– Happy Graduation!!!!!!!!
Remember to send me your e-mail address from college!!!!! I'll miss you!!!
Friday, 5/20 Return Exams? Class Party? Pot luck? Sign yearbooks?
Non-Seniors: Continue to work on Vector Worksheet
Monday, 5/23
F Non-Seniors: Continue to work on Vector Worksheet
Tuesday/Wednesday/Thursday, 5/24,5/25, 5/26
FINAL EXAM TODAY!!!!!
TURN IN VECTOR WORKSHEET AT THE BEGINNING OF CLASS (WORTH 1,000 POINTS)
FINAL EXAM WORTH 3,000 POINTS ….. 25 QUESTIONS ….. VECTORS
See you next year!!!!!! I look forward to seeing ALL OF YOU in HL MATH next year.
Don't forget to sign up to be my aide if it fits into your schedule!!!!!!
Have a great summer. E-mail me if you get bored.